This article introduces binary options and provides several pricing spreadsheets.

Binary options give the owner a fixed payout (which does not vary with the price of the underlying instrument) or nothing at all. Most Binary options are European-style; these are priced with closed-form equations derived from a Black-Scholes analysis, with the payoff determined at expiry.

The equations used in the following spreadsheets are sourced from “The Complete Guide to Option Pricing Formulas” by Espen Gaarder Haug.

## Cash or Nothing & Asset or Nothing Options

Binary options can either be Cash or Nothing, or Asset or Nothing

- A cash or nothing call has a fixed payoff if the stock price is above the strike price at expiry. A cash or nothing put has a fixed payoff if the stock price is below the strike price.
- If the asset trades above the strike at expiry, the payoff of an asset or or nothing call is equal to the asset price. Conversely, an asset or nothing has a payoff equal to the asset price if the asset trades below the strike price.

**Download Excel Spreadsheet to Price Binary Options**

## Two-Asset Cash-or-Nothing Options

These binary options are priced across two assets. They have four variants, based upon the relationship between spot and strike prices.

**up and up**: These only pay if the strike price of both assets is below the spot price of both assets**up and down**: These only pay if the spot price of one asset is above its strike price, and the spot price of the other asset is below its strike price**cash or nothing call**: These pay a predetermined amount of the spot price of both assets is above their strike price**cash or nothing put**: These pay a predetermined amount if the spot price of both assets is below the strike prie

**Download Excel Spreadsheet to Price Two Asset Cash or Nothing Options**

**Download Excel Spreadsheet to Price C-Brick Options**

## Supershares

Supershare options are based on a portfolio of assets with shares issued against their value. Supershares pay a predetermined amount if the underlying asset is priced between an upper and lower value at expiry. The amount is usually a fixed proportion of the portfolio.

Supershares were introduced by Hakansson (1976), and are priced with the following equations.

**Download Excel Spreadsheet to Price Supershares**

## Gap Options

A Gap option has a trigger price that determines if the option will payout. The strike price, however, determines the size of the payout.

The payout of a Gap option is determined by difference between the asset price and a gap, as long as the asset price is above or below the strike price. The price and payout of a European style Gap option are given by these equations

where X_{2} is the strike price and X_{1} is the trigger price.

Consider an call option with a strike price of 30, and a gap strike of 40. The option can be exercised when the asset price is above 30, but pays nothing until the asset price is above 40.

**Download Excel Spreadsheet to Price Gap Options**